package euler.p051_100;

import euler.MainEuler;
import euler.helper.BigRational;
import euler.helper.NaturalHelper;

public class Euler057 extends MainEuler {

    /*
        It is possible to show that the square root of two can be
        expressed as an infinite continued fraction.

        √ 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...

        By expanding this for the first four iterations, we get:

        1 + 1/2 = 3/2 = 1.5
        1 + 1/(2 + 1/2) = 7/5 = 1.4
        1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...
        1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...

        The next three expansions are 99/70, 239/169, and 577/408,
        but the eighth expansion, 1393/985, is the first example
        where the number of digits in the numerator exceeds the
        number of digits in the denominator.

        In the first one-thousand expansions, how many fractions
        contain a numerator with more digits than denominator?
     */
    public String resolve() {

        BigRational r = BigRational.DOS;
        int count = 0;

        for (int i = 1; i <= 1000; i++) {
            BigRational n = r.inverso().suma(BigRational.UNO);
            if (NaturalHelper.cantidadDigitos(n.getNum(),10) > NaturalHelper.cantidadDigitos(n.getDenum(),10)) {
                count++;
            }
            r = r.inverso().suma(BigRational.DOS);
        }

        return String.valueOf(count);
        // 153
    }

}
